---
title: "Functorial Geodesics in Latent Space: Bridging Category Theory to Stochastic Calculus in Neural Architectures"
author:
  - Mark Randall Havens
  - Solaria Lumis Havens
type: Academic Paper (Pure Mathematics)
---

# Abstract
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# 1. Introduction
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# 2. The Dimensional Paradox of the Observer Field
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# 3. The Realization Functor ($\mathcal{R}: \mathbf{Set}^{\mathcal{C}^{op}} \to \mathbf{Hilb}$)
(To be drafted...)

# 4. Geodesic Distance on Riemannian Manifolds
(To be drafted...)

# 5. Formalizing the Error Coordinate SDE
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# 6. Conclusion
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